Australia's government sucks ass, yes. But Fastmail seems focused on its product and has been conveying their positions and opposition to such legislation. Google does not do this, they run Google Suite like it's an automated hobby project. I'm quite certain that it's more likely that our data with Google would be used to provide data sets that could be used for advertising or sold/adapted to state surveillance (sensorvault anyone?). Even if it wasn't, we're still worse off when they arbitrarily suspend accounts and only provide us with outsourced customer service lacking an escalation path that only takes calls overnight.
Fastmail wrote a blog post about the law: https://fastmail.blog/2018/09/10/access-and-assistance-bill/
Not telling you it'll definitely work for you, but there is something similar out there.
- google maps
These are the two things I find more or less impossible to replace on android. For Pay, there is no alternative at all. For Maps, there is Osmand, which is good as static map, but not for finding addresses.
Mapbox does realtime traffic these days, https://benmaps.fr can show this layer (I haven't found that button in mobile view though, might need to do a pull request), as well as your local traffic authority probably or some other local companies.
Business info can be found through regular search engines, or if that is really difficult, then you can always fall back to google maps every once in a while.
Street view is not available where I live anyway, and Mapillary is doing reasonably. They also have OsmAnd integration. OpenStreetCam is another alternative.
Satellite imagery is not exclusive to google maps either, there are lots of sources for this, and often also plane-shot imagery from your local government. You can configure a layer in OsmAnd. Personally I use Bing Maps most frequently for this (not the app, just bing.com/maps) since it is a lot more smooth/lightweight than the awfully heavy google maps website. (I don't really use sat imagery on mobile anyway.)
Trip recording ("location history" in google) can be done with OsmAnd or many other apps as well. I configured it to automatically turn on when routing: then I have GPS on anyway and I might as well store the data. Often fun to see stats afterwards (max speed, avg speed, asc/descend, or sometimes it's practical to see the time it took).
I think that should cover the functionality of google maps.
Google pay I never heard of, unless you mean paying for apps in the Play Store, in which case the solution is to contact the developers directly, though they usually don't seem to care enough to get you as a customer (I tried this four times, never got a reply, thus never became a customer since quitting google play).
Hope this helps!
If you don't want to use Google Pay, can you not just carry a credit card?
It's super cheap (I prepaid for two years or something and it came out to less than $3/mo), faster than Gmail and won't kill your life.
EDIT: I hear Protonmail is also good, just use one of the two. They're great.